ISI: PAM & ASK OVER BAND-LIMITED CHANNELS

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1 ISI: PAM & ASK OVER BAND-LIMITED CHANNELS PREPARATION... 2 what is ISI?... 2 to do before the lab... 3 what we will do... 3 EXPERIMENT... 3 Bessel pulseforms... 3 Bessel sequences and eye patterns... 5 Butterworth channel... 6 what have we discovered?... 7 postscript... 7 TUTORIAL QUESTIONS... 8 Further reading copyright robert radzyner 2003 Vol D3, ch 1, rev 1.1-1

2 ISI: PAM & ASK OVER BAND-LIMITED CHANNELS ACHIEVEMENTS: discover how to transmit digital data efficiently with minimum intersymbol interference (ISI) over bandwidth constrained channels. PREREQUISITES: refer to recommendations under "preparation" ADVANCED MODULES: BASEBAND CHANNEL FILTERS, LINE-CODE ENCODER, DECISION MAKER, DIGITAL UTILITIES SCOPE: availability of a digital or PC-based scope would be an advantage for eye pattern displays PREPARATION what is ISI? In the experiment D2-06 entitled PCM-TDM, and the Lab Sheet L-54 PAM and TDM we investigated the transmission of sampled signals using amplitude modulated pulses. In these experiments the pulses used as the carriers of the sampled values were narrow rectangular pulses produced with a TWIN PULSE GENERATOR. In that work pulse distortion was not an issue since there was ample bandwidth to pass the sharp transitions. In this experiment we explore how to deal with pulse amplitude modulated (PAM) signals when the pulse streams are transmitted over real channels that have finite bandwidth. The key issue is the interference caused by overlapping sidelobes and tails affecting neighbouring pulses. This is known variously as crosstalk and intersymbol interference (ISI). ISI is a concern not only when dealing with PAM carrying analog sample values, but also in digital communications. For example, minimizing ISI in quantized PAM such as ASK, QAM and PCM gives increased margin against errors caused by noise. This allows a greater density of discrete amplitude levels, hence a greater number of bits per symbol interval. In this experiment we investigate pulse shape characteristics that facilitate transmission over bandwidth limited systems without causing ISI. We will discover how pulses with finite transition times and trailing oscillations ( ringing ) can be interwoven in rapid succession without affecting their data payload. 2 D3

3 to do before the lab This experiment can be approached as a journey of discovery, hence the probing deeper may be more interesting later. However you should do a quick refresh of the material in experiment D2-06 and Lab Sheet L-54, which deal with PAM and TDM, as well as experiment D1-02 and Lab Sheet L-36 introducing eye patterns. A brief review of the TIMS Advanced Modules User Manual for the DECISION MAKER and LINE-CODE ENCODER modules should save time at the workbench. what we will do We will begin with a fairly detailed inspection of pulseforms produced with a Bessel filter and then observe how these can produce a signal that is free of ISI when adjacent pulses overlap. Next we investigate pulseforms generated with a Butterworth filter. Unlike the Bessel case, here we have pulses with several cycles of trailing oscillations. We shall discover a technique for protecting the information payload of a pulse when overlapping occurs. Eye pattern displays will be used to investigate the range of pulse rates that can be transmitted without ISI 1. In other experiments we show how pulse shapes are manipulated to achieve higher transmission rates. Bessel pulseforms EXPERIMENT In this section we generate a periodic repetition of an isolated Bessel pulse. T1 patch up the system in Figure 1, one module at a time, starting with the VCO (on-board switch SW2 to VCO mode), then LINE-CODE ENCODER M.CLK and B.CLK, divide by 8 in DIGITAL UTILITIES, B.CLK IN & B.CLK OUT in the DECISION MAKER (the on-board SW1 may be in any position). Tune the VCO near 8000 Hz. Note that the LINE- CODE ENCODER generates a frequency division by 4 at B.CLK OUT. OUT Figure 1: set-up for displaying isolated pulseform DC systems 1 although these demonstrations are modelled at baseband, the principles apply equally with carrier D3-3

4 T2 check that the B.CLK OUT of the DECISION MAKER is a train of TTL LO pulses (the trigger range of the monostable may depend on the VCO frequency if there is no output, alter the position of the decision point control on the front panel to enable the trigger circuit). The repetition rate should be the VCO frequency divided by 32. T3 measure and note the width of the pulse from B.CLK OUT of the DECISION MAKER. Observe that the width of this pulse is fixed and not affected by the VCO frequency. 2 T4 obtain erect pulses by connecting the DECISION MAKER B.CLK OUT to the TTL inverter in the DIGITAL UTILITIES. T5 connect the inverter output to the LINE-CODE ENCODER DATA input. Display both the input and the UNI-RZ output and compare their widths as you vary the VCO frequency. Our pulse generator is now ready. You may be wondering why the LINE-CODE ENCODER is needed. In T3 and T5 you will have noticed that while the input pulse width remains constant as the VCO frequency changes, the UNI-RZ pulse width does not it varies so that it is always half the period of the bit clock. This way we ensure that the excitation pulse has the correct width when comparing bandlimited sequences and the corresponding isolated pulse shape at a selected pulse frequency (we shall be using sequences generated with half pulse line codes). T6 set the front panel switch of the BASEBAND CHANNEL FILTERS to position 3 to select the Bessel filter, and the front panel toggle switch for DC coupling. T7 with UNI-RZ 3 pulses at the input, connect the filter output through the ADDER to allow for amplitude control and DC offset correction in the usual way. The output display should have the general appearance shown in Figure 2 (pulse amplitude is around 1.6 V). T8 remove any DC offset and measure the width of the output pulseform across its base (ie. at zero volts) 4. Figure 2: Bessel pulse and eye pattern (symbol width 367µs) 2 note that we shall not be using any other functions of the DECISION MAKER its role here is merely to serve as a monostable with suitable pulse width (a TWIN-PULSE GENERATOR would be an alternative, however the pulse width is too narrow). 3 we shall be using RZ-AMI for sequences. The Uni-RZ format is required for the generation of individual pulseform snapshots. The pulseform elements are the same in both formats. 4 you may find the RZ-AMI line code with eye pattern scope triggering better suited for precision DC offset adjustment.. 4 D3

5 Bessel sequences and eye patterns We will now generate and observe PAM sequences of Bessel pulses by patching up the model of Figure 3. As we are in a digital communications context, using discrete amplitude levels, this is amplitude shift keying (ASK). We will first display sequence snapshots, then eye patterns. T9 before inserting the SEQUENCE GENERATOR set the on-board dip switch SW-2 for a short sequence (both toggles UP). T10 patch up the model of Figure 3 5. SNAPSHOT SYNCH OUT DC Figure 3: set-up for eye pattern and snapshot displays The set-up is not greatly different to that in Figure 1: a SEQUENCE GENERATOR replaces the DIGITAL UTILITIES and DECISION MAKER subsystem. Remember to change the line code to RZ-AMI (note that a TTL LO generates a zero valued RZ- AMI output). 6 T11 trigger the scope with the SYNC output of the SEQUENCE GENERATOR to generate a snapshot display of the sequence before and after the filter. T12 starting with a pulse rate around 2000 Hz, compare the appearance of the input and output sequences, and verify that you are able to easily recognize the individual symbol values in the bandlimited output. T13 vary the pulse frequency over the range Hz and note any changes you observe, especially as the symbol interval is reduced. Record the highest pulse frequency that allows you to comfortably recognize the symbols. Examine the sequence snapshot display and observe that pulseforms overlap across adjacent symbol intervals as you increase frequency toward 3000 Hz, the overlap approaches 100%. Even with an overlap of up to 100%, the appearance of the waveform is regular and individual symbols have a consistent shape and amplitude. Consider how this occurs and whether this indicates absence of ISI (this question will be resolved in T15 and T16). 5 the new set-up can be assembled without disturbing the DIGITAL UTILITIES and DECISION MAKER set-up it will be needed again. The only change required is to move the LINE-CODE ENCODER DATA input lead from the TTL inverter output to the SEQUENCE GENERATOR output. 6 in this lab we are not concerned with the properties of RZ-AMI line coding. This pulse format has been chosen as a good vehicle for presenting the eye pattern demonstrations. D3-5

6 T14 change the scope settings to display the eye pattern (use the B.CLK signal as scope trigger). Note that this is a three level display (see Figure 2). Using the longest sequence (both toggles of the on-board DIP switch SW-2 DOWN) will generate more transitions for the eye pattern. T15 repeat the steps above, and note the maximum pulse frequency for which the eye remains fully open. Compare this with the maximum frequency you determined with the snapshot display. Note how, with a fully open eye pattern only three distinct amplitude levels occur at the centre of the pulse interval, even with adjacent pulses overlapping. T16 using the observations you recorded for isolated pulses, demonstrate how 100% overlap may occur without causing ISI at the critical point for sampling and decision. T17 increase the pulse frequency further, so that the inner envelopes of the eye pattern begin to close. Propose a measure of eye closure (as a percentage or in db units). Obtain the eye closure value at three or four pulse frequencies, and plot the result as a function of frequency. Are you surprised by the outcome? Butterworth channel T18 with the set-up unchanged 7, switch to the Butterworth filter of the BASEBAND CHANNEL FILTERS module (position 2 on front panel). You may need to re-adjust the amplitude and DC offset. T19 observe the eye pattern over a range of pulse frequencies as before, and measure eye opening and frequency for the best outcome. Note that unlike the Bessel case, the eye pattern deteriorates at frequencies below and above the optimum. Experience has shown that a better eye may be obtained with a slightly modified filter response. T20 connect the RC LPF in the UTILITIES module in cascade with the Butterworth filter and repeat the above. Note that the eye pattern is not symmetrical (see Figure 4). Figure 4: Butterworth-RC pulse and eye pattern (symbol width 480µs) 7 this saves a little set-up time. More importantly, this is a better path to the desired outcome. 6 D3

7 T21 with the pulse frequency set for the best eye you can obtain (with or without the RC LPF), return to the sequence snapshot mode (scope external trigger to SEQUENCE GENERATOR SYNCH output) and note whether you are able to clearly identify the amplitudes of the individual pulse elements. T22 again, with the pulse frequency unchanged, return to the pulseform mode (just move three leads: LINE-CODE ENCODER DATA input back to TTL inverter and scope trigger; filters input back to UNI-RZ line-code output). Observe the significant trailing oscillations spanning several periods of the pulse frequency (see Figure 4: spacing between cursors is 0.96ms). T23 measure the intervals between the first few zero crossings. Note the variation and compare with the period of the eye pattern. what have we discovered? From the zero crossing measurements on the Butterworth pulseform we find that a nice eye pattern - with zero or near zero ISI occurs when the interval between particular zero crossings is equal to the pulse transmission interval, i.e. the period of the eye pattern. To see how ISI is avoided in a situation with multiple overlap of pulses, try the following exercise. Trace the pulseform of Figure 4 onto a transparent sheet, lay it carefully on top of the original with an arbitrary lateral displacement other than a multiple of 0.48ms and sketch the sum (ensure that the time axes are precisely aligned). Then repeat this with a multiple of 0.48ms and note the difference. The exercise is more satisfying if three or more pulses are used (you can also subtract). The critical point to note is the generation of values that are made up of only one non-zero contribution one for each pulse in the summation. Indeed, by now you will have realized that this process is replicating the process taking place in the scope when you trigger for an eye pattern display. Observe how the sidelobes can be seen about the zero amplitude level in the eye pattern, and compare with the Bessel eye. 8 Thus, as you see, if the pulse stream is the summation of pulses with ideal zero crossings, there will be only one non-zero contribution at the point where the critical zero crossings occur. Hence, inspection of the pulse stream at these points will be free of interference by overlapping pulses. This idea was discovered by H. Nyquist in the 1920 s in telegraphy applications, and is known as Nyquist s First Criterion. It is the key to ISI-free digital communications over channels that have limited bandwidth. postscript Comparing your observations in this experiment, you may be left with the impression that the Bessel pulseform would be the preferred choice it allowed a significantly higher pulse rate than the Butterworth case (near 50% faster), and is not sensitive to 8 note that this is a benefit of using RZ-AMI input format for this demonstration. It comes about due to the frequent strings of zero values. D3-7

8 symbol frequency. Nevertheless, from the zero crossing spacing of the Butterworth pulseform, you may have been tempted to venture an eye pattern near 4200 pulses per second 9. Indeed, you would have been rewarded with a distinct eye, possibly around 70% open or better. Inspection of the Butterworth pulseform in Figure 4 indicates that an impediment to better performance at the higher pulse frequency is the initially sluggish risetime of the leading edge. In the experiment D3-02 entitled equalization for ISI we use a PHASE SHIFTER to reduce the attack time by introducing a precursor zero crossing. Thus equalized, this pulseform provides good ISI quality at frequencies around 30% higher than Bessel. An interesting conclusion: to get the most from your digital communication system when bandwidth is in limited supply, use smart analog pulseforms to represents the digital symbols. TUTORIAL QUESTIONS Q1 Give two examples of band-limited channels commonly used for digital communication. Also, give an example of a channel that is not bandlimited. Q2 Why are rectangular pulse shapes unsuitable for efficient digital communications over band-limited channels? Indicate your understanding of the term efficient in this context. Q3 Explain why a low-pass filter is needed in baseband digital communications receivers operating over wideband channels, i.e. channels with no bandwidth constraint (such channels are usually referred to as power limited ). Hint: think about matched filters. Q4 Describe how intersymbol interference (ISI) arises in PAM and ASK systems operating over band-limited channels. Q5 At the lab bench you re-discovered Nyquist s smart idea of exploiting zero crossings to deal with the unavoidable time spreading that comes about when working with channels of limited bandwidth. In this exercise we examine some basic theory that underpins Nyquist s scheme. (a) confirm to your satisfaction that the Fourier transform of the (two-sided) frequency domain function G(f) = G 0 over B f < B, and zero at other values of f is given by g(t) = 2G 0 B sinc(2bt) where f is in Hz and sinc(u) denotes sin(πu)/( πu). Verify that the value of g(0) is the area under G(f). 9 may require the VCO s HI range (front panel toggle switch) with a frequency division by 4 (DIGITAL UTILITIES module). 8 D3

9 (b) Sketch the graph of g(t) and note the placement and spacing of the zero crossings. (c) We now generate an ASK message y(t) using the sinc function in part (a) to represent the symbol pulseform 10, i.e. y(t) = Σ k A k sinc[2b(t k/t s )] where: A k represents 11 random binary amplitudes ±A 0 ( volt ) T s is the symbol period (sec) k is an integer representing the symbol index Note that this expression reflects the scenario we had in the lab, where we were free to set the pulse rate with the VCO, i.e. we could tune the VCO for the desired value of symbol interval T s. Let s do this here. An interesting possibility is to have T s = 1/(2B). Substitute this in the expression for y(t), and show that at values t m of t such that 2Bt m is an integer m, all the terms in the summation except one vanish, and y(t m ) = A m. Moreover, satisfy yourself that for non integer values of 2Bt, y(t) is the summation 12 of a large number of contributions. Compare this with your observations in the lab. Note that setting T s to integer multiples of 1/(2B) will also yield the same outcome, however this is of no practical interest since we will prefer to use the highest available symbol rate, i.e. two symbols per second per Hz of bandwidth. (d) It turns out that the bandwidth efficiency of two symbols per second per Hz in part (c) is the highest that can be achieved for band-limited PAM free of ISI. Many band-limited basic pulses with suitable zero crossings exist, however the product of zero crossing interval and bandwidth will be greater than 2. Thus, the sinc pulseform represents a theoretical benchmark for bandwidth efficiency for band-limited PAM and ASK free of ISI or information loss. Is it possible to prove this in a simple way? Here is an interesting demonstration. We consider the alternating ASK sequence, +A 0, -A 0, +A 0, -A 0, +A 0, -A 0, +A 0, -A 0, using any symbol pulseform with symbol interval T s. Show that this waveform has a line spectrum (i.e. a Fourier series). What is the frequency of 10 while the sinc function is unrealisable, practical approximations are readily generated. However, as will be seen in the experiment ISI: Pulse shaping for band-limited channels, some of its characteristics are undesirable for practical applications. 11 sometimes there is a stipulation that the A k s be uncorrelated. If correlation is present (e.g. through line-code encoding) the spectrum of y(t) will not be the same as the spectrum of the basic pulse; however, for this exercise, the only parameter of interest is the bandwidth, which is not affected. 12 students interested in the mathematical niceties might be tempted to examine the convergence (or otherwise) of even one such summation. If you are not happy with the behaviour of the sinc function, you could treat it as a limiting case of a vestigial symmetry Nyquist pulseform this is normally covered in most basic texts that include the Nyquist scheme. D3-9

10 the fundamental? We now consider the transmission of this message over a baseband channel with infinite attenuation above f c Hz. What is the minimum value of T s for which any component of the message can pass through the channel? This sequence is a member of the set of binary message sequences that may occur. We assert that if a channel of bandwidth slightly less than B = f c = 1/(2 T s ) Hz does not pass this message, then the minimum bandwidth needed for transmission without distortion or information loss is B = 1/(2 T s ). Mathematicians are generally more comfortable with this kind of argument than engineers what do you think? Q6 Imagine a student who has already completed an experiment with the DECISION MAKER but has not come across Nyquist eye patterns that you generated in this lab. Show your colleague how to position the trigger instants for a decision device so that interference from adjacent symbols is minimized. Further reading Most standard textbooks cover the basics of the Nyquist theory. For an excellent and particularly insightful presentation, look up Introduction to signal transmission by W.R. Bennett, if you are lucky enough to find a copy in your library (McGraw-Hill, 1970). 10 D3

EE 400L Communications. Laboratory Exercise #7 Digital Modulation

EE 400L Communications. Laboratory Exercise #7 Digital Modulation EE 400L Communications Laboratory Exercise #7 Digital Modulation Department of Electrical and Computer Engineering University of Nevada, at Las Vegas PREPARATION 1- ASK Amplitude shift keying - ASK - in